Yes it works, I play Pac Man Vs. all the time still using the connection cable. You have a cable with a gamcube port on one end and a GBA link on the other. I don't see why it wouldnt work with most link games. Most of the link games to the gamecube is for bonus material in a gamecube game, or for link exlcusive games where you can't play the game without the GBA. The games that should always work are the GC disk games including Link options.
There might be a few games that come from the GBA and are played on the GC this could be an issue because you have no real GC start menu or options to load this.
Besides the lack of the start menu, the GC is pretty much a standalone setup in the Wii, It's not emulation alone. You physically have a gamecube built into the Wii. Anything that Gamecube could do the Wii can do with Gamecube games.
The only issues you will ever run into is some of the online "yes gamecube had online but very few just the phantasy star series" But alot of popular games like Mario Kart Double Dash and Kirbys air ride support Lan setups. With the Wii I haven't had alot of success getting the Gamecube to connect to the internet "via warppipe" a tunneling site to play MKDD online. Still if your this much of a geek to go out buy the lan adapter join a site to setup lan partys you probably still have your gamecube anyways and this is not an issue...lol